Search

Introducing post-transition metal cations is an excellent strategy for enhancing optical properties. This paper focuses on four isomers, namely the X2PO4I (X = Pb, Sn, Ba, and Sr) series. For the first time, the paper’s attention is paid to the changes in electronic structure, as well as refractive indices and birefringence, with and without the inclusion of spin–orbit effects in this series. The first-principles results show that spin–orbit effects of the 5p and 6p states found in these compounds lead to splitting of the bands, narrowing of the band gap, enhancement of the lone-pair stereochemistry, and enhancement of the refractive indices and birefringence. Moreover, a comparison of the lone-pair electron phosphates, X2PO4I (X = Pb and Sn), and the isomeric alkaline earth metal phosphates, X2PO4I (X = Ba and Sr), reveals that changes in the band structure have a greater effect on the enhancement of the birefringence than the slight enhancement of the lone-pair stereochemical activity. This study has important implications for a deeper understanding of the optical properties of crystals and the design of novel optical materials.

Transition-metal-doped clusters have long been attracting great attention due to their unique geometries and interesting physical and/or chemical properties. In this paper, the geometries of the lowest- and lower-energy CoKn (n = 2–12) clusters have been screened out using particle swarm optimization and first principles relaxation. The results show that except for CoK2 the other CoKn (n = 3–12) clusters are all three-dimensional structures, and CoK7 is the transition structure from which the lowest energy structures are cobalt atom-centered cage-like structures. The stability, the electronic structures, and the magnetic properties of CoKn clusters (n = 2–12) clusters are further investigated using the first principles method. The results show that the medium-sized clusters whose geometries are cage-like structures are more stable than smaller-sized clusters. The electronic configuration of CoKn clusters could be described as 1S1P1D according to the spherical jellium model. The main components of petal-shaped D molecular orbitals are Co-d and K-s states or Co-d and Co-s states, and the main components of sphere-like S molecular orbitals or spindle-like P molecular orbitals are K-s states or Co-s states. Co atoms give the main contribution to the total magnetic moments, and K atoms can either enhance or attenuate the total magnetic moments. CoKn (n = 5–8) clusters have relatively large magnetic moments, which has a relation to the strong Co-K bond and the large amount of charge transfer. CoK4 could be a magnetic superatom with a large magnetic moment of 5 μB.

Two-dimensional (2D) materials have attracted considerable attention due to their potential for generating ultrafast pulsed lasers. Unfortunately, the poor stability of most layered 2D materials under air exposure leads to increased fabrication costs; this has limited their development for practical applications. In this paper, we describe the successful preparation of a novel, air-stable, and broadband saturable absorber (SA), the metal thiophosphate CrPS4, using a simple and cost-effective liquid exfoliation method. The van der Waals crystal structure of CrPS4 consists of chains of CrS6 units interconnected by phosphorus. In this study, we calculated the electronic band structures of CrPS4, revealing a direct band gap. The nonlinear saturable absorption properties, which were investigated using the P-scan technique at 1550 nm, revealed that CrPS4-SA had a modulation depth of 12.2% and a saturation intensity of 463 MW/cm2. Integration of the CrPS4-SA into Yb-doped fiber and Er-doped fiber laser cavities led to mode-locking for the first time, resulting in the shortest pulse durations of 298 ps and 500 fs at 1 and 1.5 µm, respectively. These results indicate that CrPS4 has great potential for broadband ultrafast photonic applications and could be developed into an excellent candidate for SA devices, providing new directions in the search for stable SA materials and for their design.

The (strong) slope conjecture relates the degree of the col- ored Jones polynomial of a knot to certain essential surfaces in the knot complement. We verify the slope conjecture and the strong slope con- jecture for 3-string Montesinos knots satisfying certain conditions. [ABSTRACT FROM AUTHOR]